"What's up?" not "I missed you so badly"
The day has gone splendid for you! Not only did you drop your child off at day care without any issues, but you got all the items on your to do list taken care of. Groceries, mailing back that amazon return that you thought was the correct size but wasn't, grabbing your drill back from your dad because short term memory caused him to forget he had it, office depot because you can...and now its time to snag the kid.
Maybe you were thinking of your kid the whole day. "I wonder how she's doing?" "Does she have enough food packed?" "I hope she has not thrown any fits?" Definitely could be what happens the first few times you and your child separate. No matter how much you miss them though, this should NOT be reflected when you greet your child. Ted advocates for avoiding overt expressions of affection. What is overt? "I was so lonely without you!" or "I missed you so so much!", all the meanwhile hugging and showering with kisses. Think about the tone this will set with your child. "Wow, I didn't realize it but I missed my mommy and daddy too! I don't ever want to miss them again!" It seems far fetched, but the example you set will either make your children be strong enough to fend for themselves for a couple of hours, or catch the slippery slope down to never leaving your side.
Ultimately, the rules that we discussed in dropping off your kids are going to mirror the rules Ted lays out in picking your kids up. It boils down to how you, as the adult, present the situation to your young one. If you want a smooth transition, well you should act smooth. You should not make it a big deal, you should act as if this is just a regular event, and you should act as if to convey this temporary separation is only temporary. The ball is mostly in your court on this one, so have the fortitude to command control of the drop off. Pretty soon, the real challenge will be not dropping them off, but trying to pick them up after "Create Your Own Pizza" day.